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Question 675774: v=(4,2) Directrix : y=5 (this is the given information)
I get focus is 4,1
and this is the formula I come up with
(x-4)^2=12(y-2)
y=1/12(x-4)^2+2
BUT.........When I put this answer into wolfframAlpha to check it I get the focus and the directrix flipped! Does anyone know why that happens?
it gives the focus as 4,5 and the directrix as -1y
Am I doing something wrong? how does the equation know show where the focus and the directrix are located?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! v=(4,2) Directrix : y=5
This is a parabola that opens downwards.
Its standard form of equation: (x-h)^2=-4p(y-k), (h,k)=(x,y) coordinates of vertex
given coordinates of the vertex:(4,2)
axis of symmetry: x=2
focus:(4,-1) (3 units below vertex on the axis of symmetry)
p=3 (distance from directrix to vertex on the axis of symmetry)
4p=12
equation:
(x-4)^2=-12(y-2)
note:The directrix is always located on the opposite side the parabola is facing and the focus is on the side the parabola is facing, both p-distance from the vertex on the axis of symmetry.
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